An Ab-Initio Approach to Pairing Phenomena Using Modern Effective Interactions

Language:

English

Abstract:

The Unitary Correlation Operator Method (UCOM) and the Similarity Renormalization Group (SRG) allow the derivation of `tamed' phase-shift equivalent nucleon-nucleon interactions which are a suitable starting point for a wide array of many-body methods, from simple mean-field approaches like Hartree-Fock to the exact No-Core Shell Model. While the UCOM and the SRG are conceptually very different, we explicitly show that the generators of both types of unitary transformations have the same structure, and therefore treat the same kind of physics, i.e., the short-range central and tensor correlations induced by realistic nucleon-nucleon interactions. Mean-field calculations with the correlated interaction V_UCOM yield bound nuclei over the whole mass chart, and by including long-range correlations which are not explicitly described by the UCOM transformation in many-body perturbation theory, very good agreement with experimental binding energies is achieved. In conventional approaches, this is only possible by using phenomenological interactions which are explicitly tailored to mean-field calculations and therefore unable to describe nucleon scattering phase shifts. To extend our calculations to open-shell nuclei and allow for the treatment of pairing phenomena, we develop a fully consistent Hartree-Fock-Bogoliubov (HFB) approach in this work. Exact and approximate projection techniques are generalized to a simultaneous restoration of the neutron and proton number symmetries, which are broken by the introduction of quasiparticles in the HFB method. The use of V_UCOM in this framework enables us to study the pairing properties of nuclei from first principles, and provides insight into the effect of short-range correlations on the pair formation. We present results from the application of the HFB method with and without projection to the study of the tin isotopic chain. While the effect of three-nucleon forces on the binding energies can be minimized by an appropriately chosen UCOM transformation, the HF and HFB ground states calculated with such a two-body interaction exhibit too-small radii and a low level density, which are caused by the strong non-locality of the corresponding V_UCOM. Naturally, the low level density is found to be a strong impediment to pairing. In exploratory HF calculations, a three-nucleon contact force was able to improve the radii and level densities. Since the use of such a force in HFB calculations is more demanding, we approximate it by a zero-range density-dependent two-body interaction in order to assess the impact of three-nucleon effects in our HFB framework. The ground states obtained from the HFB method serve as the basis for a fully self-consistent Quasiparticle Random Phase Approximations (QRPA), which can be used to study pairing effects on collective excitations. We present selected results on electromagnetic resonances in the tin isotopes, in particular the pygmy dipole resonance in the neutron-rich isotopes Sn-130 and Sn-132. In addition, we apply the charge-exchange version of our QRPA to the isobaric analog and Gamow-Teller resonances in Zr-90.